Two protons exerts a nuclear force on each other, the distance between them is

From the relation $R=R_{0} A^{1 / 3},$ where $R_{0}$ is a constant and $A$ is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of $A$).

Highly energetic electrons are bombarded on a target of an element containing $30$ neutrons. The ratio of radii of nucleus to that of Helium nucleus is ${14^{1/3}}$. The atomic number of nucleus will be

If the total binding energies of ${ }_1^2 H ,{ }_2^4 He ,{ }_{26}^{56} Fe$ and ${ }_{92}^{235} U$ nucleiare $2.22,28.3,492$ and $1786 MeV$ respectively, identify the most stable nucleus of the following.

Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6 \times 10^{-27}\,kg$ and radius of nucleus is $1.5 \times 10^{-15} A ^{1 / 3}\,m$. The approximate ratio of the nuclear density and water density is $n \times 10^{13}$. The value of $n$ is $.................$

Write and explain the Einstein theory of special relativity.